Change object origin precisely?
There a couple of ways:


Tool shelf > Tools [tab] > Set Origin > Origin to Geometry or Origin to Center of Mass (which could be the same depending on your object)
You can move the 3D cursor to any point related to the object mesh. In edit mode, snap it to any point of the object mesh, or the mean point of any selection within the mesh, like this: Shift+S > Cursor to Selected or Active or Center.  Then tab back to object mode and as in #1 ... Set Origin > Origin to 3D Cursor